Question

The variables x and y satisfy the equation 5^(y+1) = 2^(3x)

By taking logarithms, show that the graph of y against x is a straight line.

ii) Find the exact value of the gradient of the line and state the coordinates of the point at whch the line cuts the y-axis.

Answer 1

@Hayhayz Another one she didn't teach us :o

Answer 2

If I may help?

Answer 3

If you please.

Answer 4

With my pleasure!

Answer 5

Can you apply log to both sides with any base you want?

Answer 6

I have no idea..

Answer 7

\[\Large 5^{(y+1)} = 2^{(3x)}\]
Is that your equation?

Answer 8

Yes.

Answer 9

Nice!

Answer 10

you can use logs to help you here

Answer 11

Do I like ln both sides to move the exponents to the front?

Answer 12

Take log (standard log with base of 10) for both side, you get:
\[\Large \log[5^{(y+1)}] = \log[2^{(3x)}]\]

Answer 13

yup u got it

Answer 14

remember log(A^Y) = y log(A)

Answer 15

And one of the properties of logarithm's is
\[\huge \log(x^a)=alogx\]

Answer 16

I got:
(y + 1)log (5) = (3x)log (2)

Answer 17

Great!

Answer 18

if you proved log(A*B) = log(A)+LOG(B)
then you can easily see that
log(A^N) = log(A*A*A*A*A..) = LOG(A) + LOG(A) + LOG(A)+... = n log (A)

Answer 19

Thank you for the medal!

But let's finish it firstly

Answer 20

or y = ?

Answer 21

\[\Large (y+1)*\log[5] = (3x)\log[2]\]
then
\[\Large (y+1)= (3x)\frac{ \log[2] }{ \log[5] }\]
then
\[\Large (y+1)= const*(3x)\]
then
\[\Large y+1= const*x\]
then
\[\Huge y= const*x-1\]

which is an equation of straight line

Answer 22

I hope I helped you.

Answer 23

Wonderful, I got that, but didn't put the "constant" part.

Answer 24

Thank you for your appreciation!
You can calculate it easily I think!

Answer 25

I did 3x - log(2)/log(5) - 1
3x - 0.5693 and so on.

Answer 26

algebra looks wrong

Answer 27

log(2)/log(5)=?

Answer 28

0.43067?

Answer 29

0.43067*3=?

Answer 30

AH

Answer 31

I think you got it!

Answer 32

y = 3x - 0.292?

Answer 33

y=(0.43067*3)x-1

Answer 34

Oh, I get it now, that's what confused me.

Answer 35

How would you find the gradient, isn't it the m value?

Answer 36

1.292?

Answer 37

Yes it is the slope/the gradient = 1.292

Brilliant!

Answer 38

So for the y-intercept, all I would have to do is plug in 0 for x and get y = -1?
The cords would be (0, -1) ?

Answer 39

Excellent!
I think you got it!

Answer 40

Wonderful, thank you so much.

Answer 41

You are welcome!
Any Help... Any Time...
Thank you for learning!

Answer 42

Do you have any more questions?

Answer 43

Actually, there's one in my notes I never finished. Want me to tag you?

Answer 44

If you need a help and if I am not bothering you!

Answer 45

Do you mind if I just type in out right now?

Answer 46

It is given that ln(y+1) - lny = 1 +3lnx. Express y in terms of x, in a form not involving logarithms.

Answer 47

Can we start in new post, please?

Answer 48

Yes, of course.

Answer 49

Welcome!